This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A380017 #10 Jan 23 2025 04:47:54
%S A380017 1,1,6,55,716,12085,250726,6172915,175903400,5694587209,206438732810,
%T A380017 8284550317351,364605758728828,17461047965591581,903964982917764782,
%U A380017 50306323769422679995,2994799872257498255696,189906103853462927405329,12779300537432602189228306
%N A380017 Expansion of e.g.f. 1/(1 - 3*x*exp(x))^(1/3).
%F A380017 a(n) = n! * Sum_{k=0..n} (-3)^k * k^(n-k) * binomial(-1/3,k)/(n-k)!.
%F A380017 a(n) ~ sqrt(2*Pi) * n^(n - 1/6) / (Gamma(1/3) * (1 + LambertW(1/3))^(1/3) * exp(n) * LambertW(1/3)^n). - _Vaclav Kotesovec_, Jan 23 2025
%o A380017 (PARI) a(n) = n!*sum(k=0, n, (-3)^k*k^(n-k)*binomial(-1/3, k)/(n-k)!);
%Y A380017 Cf. A006153, A380015, A380019.
%K A380017 nonn
%O A380017 0,3
%A A380017 _Seiichi Manyama_, Jan 09 2025